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Median of Two Sorted Arrays in C++
Suppose we have two arrays; these arrays are sorted. So we have to find the median of these two arrays. So if the arrays are like [1,5,8] and [2,3,6,9], then the answer will be 5.
To solve this, we will follow these steps −
Define a function findMedianSortedArrays, this will take nums1 and nums2 arrays
if size of nums1 > size of nums2, then,
Call the function return findMedianSortedArrays(nums2, nums1)
x := size of nums1, y := size of nums2
low := 0, high := x
totalLength := x + y
while low<=high, do −
partitionX := low + (high - low) / 2
partitionY := (totalLength + 1) / 2 - partitionX
maxLeftX = -inf when partitionX is 0, otherwise nums1[partitionX-1]
maxRightX = inf when partitionX is x, otherwise nums1[partitionX]
maxLeftY = -inf when partitionY is 0, otherwise nums2[partitionY-1]
maxRightY = inf when partitionY is y, otherwise nums2[partitionY]
if maxLeftX<=minRightY and maxLeftY <= minRightX, then,
if totalLength mod 2 is same as 0, then,
return (maximum of maxLeftX and maxLeftY) + minimum of minRightX and minRightY) / 2
Otherwise
return maximum of maxLeftX and maxLeftY
Otherwise when maxLeftX>minRightY, then −
high := partitionX - 1
Otherwise low := partitionX + 1
return 0
Example (C++)
Let us see the following implementation to get better understanding −
#include <bits/stdc++.h>
using namespace std;
class Solution {
public:
double findMedianSortedArrays(vector& nums1, vector<int>& nums2) {
if(nums1.size()>nums2.size())
return findMedianSortedArrays(nums2,nums1);
int x = nums1.size();
int y = nums2.size();
int low = 0;
int high = x;
int totalLength = x+y;
while(low<=high){
int partitionX = low + (high - low)/2;
int partitionY = (totalLength + 1)/2 - partitionX;
int maxLeftX = (partitionX ==0?INT_MIN:nums1[partitionX1] );
int minRightX = (partitionX == x?INT_MAX :
nums1[partitionX]);
int maxLeftY = (partitionY ==0?INT_MIN:nums2[partitionY1] );
int minRightY = (partitionY == y?INT_MAX : nums2[partitionY]);
if(maxLeftX<=minRightY && maxLeftY <= minRightX){
if(totalLength% 2 == 0){
return ((double)max(maxLeftX,maxLeftY) + (double)min(minRightX,minRightY))/2;
} else {
return max(maxLeftX, maxLeftY);
}
}
else if(maxLeftX>minRightY)
high = partitionX-1;
else low = partitionX+1;
}
return 0;
}
};
main(){
Solution ob;
vector<int> v1 = {1,5,8}, v2 = {2,3,6,9};
cout << (ob.findMedianSortedArrays(v1, v2));
}Input
[1,5,8] [2,3,6,9]
Output
5
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